A simple average gives every observation one equal vote; a weighted average gives each value a stated weight. Scores of 90 and 70 average to 80 when equally weighted, but a 90 on 1 credit and 70 on 3 credits produce 75 because (90×1 + 70×3) divided by 4 equals 75. The weight must represent a real amount.
What is the difference between an average and a weighted average?
A student earns 90 in a 1-credit course and 70 in a 3-credit course. The simple mean is (90 + 70) / 2 = 80. The credit-weighted mean is (90×1 + 70×3) / (1+3) = 300/4 = 75. The second value answers the transcript question because four credits, not two course names, make up the total.
When is equal weighting wrong?
List each value, its weight, and the common unit of the weights. Multiply each value by its weight, add those products, then divide by total weight. The weighted-average calculator checks a two-value case. Use an ordinary arithmetic mean only when every observation has equal importance by the question’s definition.
How do I calculate a weighted average?
Weights can be credits, quantities sold, time, frequency, or population counts, but percentages must be converted consistently. Two values with weights 25% and 75% can use 0.25 and 0.75, whose total is 1, or 25 and 75, whose total is 100. The weighted result should lie between the smallest and largest input when all weights are non-negative.
What should weighted-average weights add up to?
Do not divide weighted products by the number of rows instead of total weight. Do not average averages without the group sizes that produced them. Do not use values such as “high” and “low” as if they were numeric intervals. Do not enter 25 and 75 as weights while also treating them as percentages twice.
When does a weighted average need more context?
A weighted average summarizes a declared rule; it does not prove that the rule is fair, predictive, or statistically representative. Missing observations, biased samples, changing weights, and non-linear grading rules can require another method. Keep the source and meaning of every weight with the reported average.
Source for the external fact
OpenStax identifies the weighted mean as a distinct measure of central tendency in its statistics key terms, so an average must state whether equal weighting was intended.
Related calculators
Calculate unequal-credit results in the weighted-average tool, inspect a grade calculation in the GPA calculator, and use the percentage tool to check a weight share.